Multiply the following complex numbers: $({-5+4i}) \cdot ({-3+5i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5+4i}) \cdot ({-3+5i}) = $ $ ({-5} \cdot {-3}) + ({-5} \cdot {5}i) + ({4}i \cdot {-3}) + ({4}i \cdot {5}i) $ Then simplify the terms: $ (15) + (-25i) + (-12i) + (20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 15 + (-25 - 12)i + 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 15 + (-25 - 12)i - 20 $ The result is simplified: $ (15 - 20) + (-37i) = -5-37i $